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4.3 Isosceles & Equilateral Triangles

4.3 Isosceles & Equilateral Triangles. Geometry Big Daddy Flynn 2013.

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4.3 Isosceles & Equilateral Triangles

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  1. 4.3 Isosceles & Equilateral Triangles Geometry Big Daddy Flynn 2013

  2. In lesson 4.1, you learned that a triangle is an isosceles if it has at least two congruent sides. If it has exactly two congruent sides, then they are the legs of the triangle and the non-congruent side is the base. The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle. Using properties of Isosceles Triangles

  3. 4.6 Base Angles Theorem: If two sides of a triangle are congruent, then the angles opposite them are congruent. If AB ≅ AC, then B ≅ C. Theorems 73º 73º

  4. 4.7 Converse of the Base Angles Theorem: If two angles of a triangle are congruent, then the sides opposite them are congruent. If B ≅ C, then AB ≅ AC. Theorems 12 cm 12 cm

  5. An EQUILATERAL triangle is a special type of isosceles triangle. The corollaries below state that a triangle is EQUILATERAL if and only if it is EQUIANGULAR. Corollary to theorem 4.6—If a triangle is equilateral, then it is equiangular. Corollary to theorem 4.7– If a triangle is equiangular, then it is equilateral. Remember:

  6. Find the value of x Find the value of y Solution a: How many total degrees in a triangle? This is an equilateral triangle which means that all three angles are the same. 3x = 180 – Triangle Sum Theorem. X = 60 Ex. 2: Using Equilateral and Isosceles Triangles y° x°

  7. Find the value of x Find the value of y Solution b: How many total degrees in a line? The triangle has base angles of y° which are equal. (Base Angles Theorem). The other base angle has the same measure. The vertex angle forms a linear pair with a 60° angle, so its measure is 120° 120° + 2y° = 180°(Triangle Sum Theorem) 2y = 60 (Solve for y) y = 30 Ex. 2: Using Equilateral and Isosceles Triangles y° x° 60°

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